This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

Can you cut up a square in the way shown and make the pieces into a triangle?

Follow these instructions to make a five-pointed snowflake from a square of paper.

Follow these instructions to make a three-piece and/or seven-piece tangram.

It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!

Can you make five differently sized squares from the interactive tangram pieces?

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

Reasoning about the number of matches needed to build squares that share their sides.

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?

Exploring and predicting folding, cutting and punching holes and making spirals.

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?

Using these kite and dart templates, you could try to recreate part of Penrose's famous tessellation or design one yourself.

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

Did you know mazes tell stories? Find out more about mazes and make one of your own.

Make a cube out of straws and have a go at this practical challenge.

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

Make a flower design using the same shape made out of different sizes of paper.

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.

How can you make a curve from straight strips of paper?

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

Can you visualise what shape this piece of paper will make when it is folded?

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

What shape is made when you fold using this crease pattern? Can you make a ring design?

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

Make a mobius band and investigate its properties.

Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

Can you make the birds from the egg tangram?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

Ideas for practical ways of representing data such as Venn and Carroll diagrams.

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.

In this article for primary teachers, Fran describes her passion for paper folding as a springboard for mathematics.

Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?